# Review Questions for Errors and Complexity

- What is the formula for relative error?
- What is the formula for absolute error?
- Which is usually the better way to calculate error?
- If you have k accurate significant digits, what is the tightest bound on your relative error?
- Given a maximum relative error, what is the largest (or smallest) value you could have?
- How do you compute relative and absolute error for vectors?
- What is truncation error?
- What is rounding error?
- What does it mean for an algorithm to take \(\mathcal{O}(n^3)\) time?
- Can you give an example of an operation that takes \(\mathcal{O}(n^2)\) time?
- What does it mean for error to follow \(\mathcal{O}(h^4)\)?
- Can you simplify \(\mathcal{O}(h^5 + h^2 + h)\)? What assumption do you need to make?
- If you know an operation is \(\mathcal{O}(n^4)\), can you predict its time/error on unseen inputs from inputs that you already have?
- If you are given runtime or error data for an operation, can you find the best \(x\) such that the operation is \(\mathcal{O}(n^x)\)?
- What is algebraic growth/convergence?
- What is exponential growth/convergence?